This study is for individuals who have peritoneal mesothelioma, a cancer of the lining of your abdominal wall and organs (the peritoneum). Doctors leading the study would like to determine the effects of treating this cancer with immunotherapy drugs (nivolumab and ipilimumab - the two study drugs that will be used in this study) before and after surgery.

Doctors hope to learn if giving these two drugs before surgery will decrease the amount of viable (live) cancer cells that remain at the time of surgery and whether it will delay the time it could take for the cancer to regrow.

Inclusion Criteria:

1. Have a diagnosis of histologically or cytologically confirmed peritoneal mesothelioma, of epithelial, biphasic, or sarcomatoid subtypes
2. Have disease burden amenable to cytoreduction and hyperthermic intraperitoneal chemotherapy (HIPEC), as determined by a surgeon specializing in mesothelioma
3. Have measurable or evaluable disease based on RECIST 1.1 or on laparoscopy
4. Have no definitive evidence of visceral metastases by best staging
5. Be willing to undergo laparoscopy or mini-laparotomy for peritoneal staging
6. Adequate organ function as determined by screening labs,
7. Have an ECOG performance status of < 2
8. Be 18 years of age on day of signing informed consent
9. Be willing and able to provide written informed consent for the trial

Exclusion Criteria:

1. Is currently participating in a study of an investigational agent and received an investigational agent within 4 weeks of the first dose of treatment on this protocol

2. Has received any immunotherapy agents outside of this protocol within 4 weeks of the first dose of treatment on this protocol

3. Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (>10 mg of prednisone daily or equivalent) or any other form of immunosuppressive therapy within 14 days prior to the first dose of study drug.

4. Has a known history of active TB infection (Bacillus tuberculosis)

5. Has active COVID-19 infection

6. Has known history of, or any evidence of active, non-infectious pneumonitis that required steroids, or active pneumonitis

7. Has a severe hypersensitivity to nivolumab or any of its excipients

8. Has a severe hypersensitivity to ipilimumab or any of its excipients

9. Has an active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs)

10. Has a known additional malignancy that is progressing or required active treatment within the 3 years prior to enrollment - exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer or other tumors that will not affect life expectancy

11. Has an active infection requiring systemic therapy

12. Has a known history of HIV, Hepatitis B, or Hepatitis C

13. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.

14. Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the screening visit through 120 days after the last dose of trial treatment

    1. Female subjects of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required.
    2. Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication (Reference Section 5.8.2). Subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for > 1 year.
    3. Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy.

15. Is on anticoagulation that cannot be discontinued in the perioperative period

16. Has received a live vaccine within 30 days of planned start of study therapy

12 weeks